Estimating the Elevation of a Wireless Terminal by Determining a Bias of Pressure Measurement from a Probability Distribution

ABSTRACT

A location engine that generates an estimate of the measurement bias of the pressure sensor in a wireless terminal. The estimate is determined from a probability distribution characterized as having a flat top with exponentially decaying sides. The probability distribution is generated by inferring i) a range of elevations within which the wireless terminal is most likely present, wherein the elevations have associated barometric pressures, and ii) a corresponding range of measurement biases based on an inferred range of the barometric pressures. The location engine updates the probability distribution over time. The location engine makes a single estimate of measurement bias available by determining a mean of the updated probability distribution, such as an average of the low and high endpoints that define the flat top. Subsequently, the location engine generates an estimate of the elevation of the wireless terminal by accounting for the estimate of measurement bias.

FIELD OF THE INVENTION

The present invention relates to telecommunications in general and, moreparticularly, to a technique for determining the bias of pressuremeasurement of a wireless terminal from a probability distribution, andestimating the elevation of the wireless terminal by correcting for thebias.

BACKGROUND OF THE INVENTION

The salient advantage of wireless telecommunications over wirelinetelecommunications is that the user of the wireless terminal is affordedthe opportunity to use his or her terminal anywhere. On the other hand,the salient disadvantage of wireless telecommunications lies in thatfact that because the user is mobile, an interested party might not beable to readily ascertain the location of the user.

Such interested parties might include both the user of the wirelessterminal and a remote party. There are a variety of reasons why the userof a wireless terminal might be interested in knowing his or herlocation. For example, the user might be interested in telling a remoteparty where he or she is or, alternatively, the user might seek advicein navigation.

In addition, there are a variety of reasons why a remote party might beinterested in knowing the location of the user. For example, therecipient of an E 9-1-1 emergency call from a wireless terminal might beinterested in knowing the location of the wireless terminal so thatemergency services vehicles can be dispatched to that location.

There are many techniques in the prior art for estimating the locationof a wireless terminal with regard to its latitude and longitude. Inaccordance with some techniques, the location of a wireless terminal isestimated, at least in part, from signal measurements that are reportedby the wireless terminal. The reported measurements are of signalsmeasured by the wireless terminal that are transmitted by one or morebase stations and/or by Global Navigation Satellite System (GNSS)satellites, such as Global Positioning System (GPS) satellites. In orderfor these techniques to work, at least some of the transmitted signalshave to be strong enough to allow for accurate measurement by thewireless terminal and for reliable processing by the particularestimation technique. Some of these techniques work well even inenvironments where the measured strengths of the different signals varysignificantly, such as where signal obstructions are present, includingnatural obstructions such as mountains and artificial obstructions suchas buildings.

There are also techniques in the prior art for estimating the elevationof a wireless terminal. Some of these techniques rely on therelationship between barometric pressure, P_(OBJ), and elevation,Z_(OBJ), according to the formula:

$\begin{matrix}{Z_{OBJ} = {{{- H_{OUT}} \cdot {\ln ( \frac{P_{OBJ}}{P_{W}} )}} + Z_{W}}} & ( {{Eq}.\mspace{11mu} 1} )\end{matrix}$

wherein:

-   -   H_(OUT) is the outdoor scale height of the atmosphere, which is        the elevation at which the atmospheric pressure has decreased to        e⁻¹ times its value at mean sea level (e.g., approximately 8400        meters) and is based on outdoor temperature at a pressure        station reference.    -   P_(OBJ) is the relevant measurement of barometric pressure at        the elevation of interest,    -   P_(W) is the measurement of atmospheric pressure at the pressure        station reference, and    -   Z_(W) is the elevation of the pressure station reference.

It is well known in the art how to estimate the elevation of an objectusing Equation 1. For example, it is well known in the art how toestimate the elevation of a wireless terminal using Equation 1, in whichbarometric pressure measurements made by the wireless terminal can beused.

In order to determine the elevation of the wireless terminal, however,it is necessary to consider various sources of error, including i) thepressure measurement bias of the wireless terminal's barometric sensordevice and ii) the pressure measurement drift of the sensor device.

The pressure measurement bias of the sensor device is typically between2 and 10 meters in height variation (versus equivalent pressurevariation) and can be as much as 40 meters in height variation. Themeasurement bias can vary across barometric sensor devices of differentmanufacturers and even across different production batches of the samemanufacturer.

The pressure measurement drift of the sensor device is typically between0 and 5 meters in height equivalent within a month and can be differentfrom one device to another. The drift can be attributed to one or moreof the aging of the measuring membrane of the electronic sensor chip,MEMS sensor temperature/humidity cycling, internal IC stresses, andplastic deformation to the sensor. Because of these error sources, thedrift (and measurement bias) can vary across wireless terminals of thesame model. The drift can also be attributed to temperature and/orhumidity considerations in the operating environment of the chip.

As can be seen in Equation 1, an incorrect value of the barometricpressure P_(OBJ) can result in an inaccurate estimate of elevation.

SUMMARY OF THE INVENTION

The present invention enables both the pressure measurement bias of andthe drift of a barometric sensor in a wireless terminal to be identifiedand compensated for, resulting in calibrated pressure measurements andan improved estimate of elevation of the wireless terminal by correctingfor the bias. In accordance with the illustrative embodiment of thepresent invention, a location engine disclosed herein generates anestimate of the measurement bias by first generating a range of possiblemeasurement biases and then constricting the range over time throughsubsequent, iterative processing.

The range of measurement biases is represented as part of a probabilitydistribution having a flat top with low and high endpoints. Although auniform distribution with the low and high endpoints might suffice undersome operating conditions, the inventors improved on this idea byincorporating exponentially decaying sides that extend from the low andhigh endpoints to the respective ends of the probability distribution.Thus, the probability distribution of the illustrative embodiment ischaracterized by four parameters: the low and high endpoints and lowerand upper uncertainties, wherein the uncertainties define the averagedecay lengths of the respective exponential sides. Such a distributionis referred to in this specification as a “low/high distribution.”

The location engine of the illustrative embodiment generates aprobability distribution of pressure measurement biases based on one ormore new measurements that it receives. Such measurements include i) anestimate of the lateral location of a wireless terminal, ii) theuncertainty of the location, iii) measurements of barometric pressurefrom a pressure reference, such as a pressure station at a nearbyairport or weather station, and iv) measurements of barometric pressurefrom the wireless terminal. With the new measurements, the locationengine generates a probability distribution by essentially inferring i)a range of elevations within which the wireless terminal is most likelypresent, wherein the elevations have associated barometric pressures,and ii) a corresponding range of measurement biases between the low andhigh endpoints based on an inferred range of the barometric pressures.The location engine makes a single measurement bias estimate availableby determining a mean of the probability distribution, such as anaverage of the low and high endpoints.

The location engine can also update a previously-generated low/highprobability distribution, as a function of time, how much the pressuremeasurement bias has drifted, or something else. If apreviously-generated probability distribution is available and is to beupdated, the location engine generates an updated probabilitydistribution by combining mathematically i) a probability distributionthat is based on one or more of the new measurements, as explainedabove, and ii) the previously-generated probability distribution. Thenew-measurement distribution and the previously-generated distributioncan be combined, for example, via addition of the logarithmicrepresentations of the two distributions with piecewise-linear fittingto transform the sum of the two distributions back into an approximatelinear representation.

There are advantages to using the low/high distribution of theillustrative embodiment and to using a probability distribution ingeneral to determine measurement bias. First, as with a uniformprobability distribution, due to its flat top, the low/high probabilitydistribution is robust to the lack of independence between measurements.In particular, processing that involves a distribution with a flat topwill not suddenly decrease the uncertainty from a large number ofhigh-uncertainty measurements, as processing involving a Gaussian-likedistribution having a peaked top would. Second, unlike the uniformdistribution, the low/high distribution elegantly and reasonably handlesthe case when the interval between the low and high endpoints of thenew-measurement probability distribution and the interval between thelow and high endpoints of the previously-generated probabilitydistribution do not have a common intersection. And third, using aprobability distribution in general provides a basis for determiningpressure measurement bias when the elevation of the wireless terminal ispresently unavailable or cannot be otherwise inferred.

A first illustrative method of estimating the elevation of a wirelessterminal, comprises: receiving, by a data processing system, a firstestimate of location of a wireless terminal; receiving, by the dataprocessing system, a first measurement of barometric pressure at thewireless terminal; generating, by the data processing system, datapoints in a nonempty first set of data points in space based on thefirst estimate of location of the wireless terminal, wherein the datapoints correspond to geographical coordinates; generating, by the dataprocessing system, a first probability distribution of pressuremeasurement bias defined by: (i) a first estimate of bias of barometricpressure measured by the wireless terminal, wherein the first estimateof bias is based on (a) a first data point whose geographicalcoordinates are at the lowest elevation in the first set of data points,and (b) the first measurement of barometric pressure at the wirelessterminal, and (ii) a second estimate of bias of barometric pressuremeasured by the wireless terminal, wherein the second estimate of biasis based on (a) a second data point whose geographical coordinates areat the highest elevation in the first set of data points, and (b) thefirst measurement of barometric pressure at the wireless terminal;receiving, by the data processing system, a second measurement ofbarometric pressure at the wireless terminal; and generating, by thedata processing system, an estimate of the elevation of the wirelessterminal based on (a) the second measurement of barometric pressure atthe wireless terminal, and (b) the first probability distribution ofpressure measurement bias.

A second illustrative method of estimating the elevation of a wirelessterminal comprises: receiving, by a data processing system, a series ofmeasurements of barometric pressure at the wireless terminal;generating, by the data processing system, a first probabilitydistribution of pressure measurement bias, based on the series ofmeasurements of barometric pressure at the wireless terminal; receiving,by a data processing system, a first estimate of location of a wirelessterminal; receiving, by the data processing system, a first measurementof barometric pressure at the wireless terminal; generating, by the dataprocessing system, data points in a nonempty first set of data points inspace based on the first estimate of location of the wireless terminal,wherein the data points correspond to geographical coordinates;generating, by the data processing system, a second probabilitydistribution of pressure measurement bias defined by: (i) a firstestimate of bias of barometric pressure measured by the wirelessterminal, wherein the first estimate of bias is based on (a) a firstdata point whose geographical coordinates are at the lowest elevation inthe first set of data points, and (b) the first measurement ofbarometric pressure at the wireless terminal, and (ii) a second estimateof bias of barometric pressure measured by the wireless terminal,wherein the second estimate of bias is based on (a) a second data pointwhose geographical coordinates are at the highest elevation in the firstset of data points, and (b) the first measurement of barometric pressureat the wireless terminal; receiving, by the data processing system, asecond measurement of barometric pressure at the wireless terminal; andgenerating, by the data processing system, an estimate of the elevationof the wireless terminal based on (a) the second measurement ofbarometric pressure at the wireless terminal, (b) the first probabilitydistribution of pressure measurement bias, and (c) the secondprobability distribution of pressure measurement bias.

A third illustrative method of estimating the elevation of a wirelessterminal, the method comprising: receiving, by a data processing system,a first estimate of location of a wireless terminal, the first estimatecomprising i) a first geographic coordinate value along a firsthorizontal dimension and ii) a second geographic coordinate value alonga second horizontal dimension; receiving, by the data processing system,a first measurement of barometric pressure at the wireless terminal;generating, by the data processing system, data points in a nonemptyfirst set of data points in space, based on i) a first normaldistribution that is defined by the first geographic coordinate valueand ii) a second normal distribution that is defined by the secondgeographic coordinate value, wherein the data points in the first setare represented by coordinate values along the first and secondhorizontal dimensions; generating, by the data processing system: (i) afirst estimate of bias of barometric pressure measured by the wirelessterminal, based on (a) a first data point whose geographical coordinatesare at the lowest elevation in the first set of data points, and (b) thefirst measurement of barometric pressure at the wireless terminal, and(ii) a second estimate of bias of barometric pressure measured by thewireless terminal, based on (a) a second data point whose geographicalcoordinates are at the highest elevation in the first set of datapoints, and (b) the first measurement of barometric pressure at thewireless terminal; receiving, by the data processing system, a secondmeasurement of barometric pressure at the wireless terminal; andgenerating, by the data processing system, an estimate of the elevationof the wireless terminal based on (a) the second measurement ofbarometric pressure at the wireless terminal, (b) the first estimate ofbias, and (c) the second estimate of bias.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a diagram of the salient components of telecommunicationssystem 100 in accordance with the illustrative embodiment of the presentinvention.

FIG. 2 depicts a block diagram of the salient components of wirelessterminal 101 of telecommunications system 100.

FIG. 3 depicts a block diagram of the salient components of locationengine 113 of telecommunications system 100.

FIG. 4 depicts a flowchart of the salient processes performed as part ofmethod 400 in accordance with the illustrative embodiment of the presentinvention.

FIG. 5 depicts a flowchart of the salient processes performed inaccordance with operation 401 of method 400.

FIG. 6 depicts a map of the ground level of geographic region 120.

FIG. 7 depicts an isometric drawing of geographic region 120, includingbuildings.

FIG. 8 depicts a three-dimensional survey of geographic region 120.

FIG. 9 depicts a flowchart of the salient processes performed inaccordance with operation 403 of method 400.

FIG. 10 depicts a flowchart of the salient processes performed inaccordance with operation 905 of method 403.

FIG. 11 depicts a flowchart of the salient processes performed inaccordance with operation 1001 of method 905.

FIGS. 12A and 12B depicts a first example of the data points generatedin accordance with operations 1101 and 1103.

FIGS. 13A and 13B depict a second example of the data points generatedin accordance with operations 1101 and 1103.

FIG. 14 depicts a flowchart of the salient processes performed inaccordance with operation 1005 of method 905.

FIGS. 15A, 15B, 15C, and 15D depict various low/high probabilitydistributions.

FIG. 16 depicts a flowchart of the salient processes performed inaccordance with operation 907.

FIG. 17 depicts a flowchart of the salient processes performed inaccordance with operation 407 and operation 903.

FIG. 18 depicts a flowchart of the salient processes performed inaccordance with operation 409.

DEFINITIONS

Barometric Pressure—For the purposes of this specification, the term“barometric pressure” is defined as a pressure measured by a barometer.This pressure relates to atmospheric pressure, which is the force perunit area exerted on a surface by the weight of the air above thatsurface in the atmosphere of Earth.

Based on—For the purposes of this specification, the phrase “based on”is defined as “being dependent on” in contrast to “being independentof”. The value of Y is dependent on the value of X when the value of Yis different for two or more values of X. The value of Y is independentof the value of X when the value of Y is the same for all values of X.Being “based on” includes both functions and relations.

Elevation—For the purposes of this specification, the term “elevation”is defined as the height relative to a reference (e.g., mean sea level,ground level, etc.).

Generate—For the purposes of this specification, the infinitive “togenerate” and its inflected forms (e.g., “generating”, “generation”,etc.) should be given the ordinary and customary meaning that the termswould have to a person of ordinary skill in the art at the time of theinvention.

Height—For the purposes of this specification, the term “height” shouldbe given the ordinary and customary meaning that the term would have toa person of ordinary skill in the art at the time of the invention.

Identity of a Radio Signal—For the purposes of this specification, thephrase “identity of a radio signal” is defined as one or more indiciathat distinguish one radio signal from another radio signal.

Lateral Location—For the purposes of this specification, a “laterallocation” is defined as information that is probative of latitude orlongitude or latitude and longitude.

Location—For the purposes of this specification, the term “location” isdefined as a zero-dimensional point, a finite one-dimensional pathsegment, a finite two-dimensional surface area, or a finitethree-dimensional volume.

Outdoor Location—For the purposes of this specification, the term“outdoor location” is defined as a location at which outdoor atmosphericpressure is able to be measured without impediment.

Processor—For the purposes of this specification, a “processor” isdefined as hardware or hardware and software that performs mathematicaland/or logical operations.

Radio—For the purposes of this specification, a “radio” is defined ashardware or hardware and software that is capable of telecommunicationsvia an unguided (i.e., wireless) radio signal of frequency less than 600GHz.

Receive—For the purposes of this specification, the infinitive “toreceive” and its inflected forms (e.g., “receiving”, “received”, etc.)should be given the ordinary and customary meaning that the terms wouldhave to a person of ordinary skill in the art at the time of theinvention.

Transmit—For the purposes of this specification, the infinitive “totransmit” and its inflected forms (e.g., “transmitting”, “transmitted”,etc.) should be given the ordinary and customary meaning that the termswould have to a person of ordinary skill in the art at the time of theinvention.

Wireless Terminal—For the purposes of this specification, the term“wireless terminal” is defined as a device that is capable oftelecommunications without a wire or tangible medium. A wirelessterminal can be mobile or immobile. A wireless terminal can transmit orreceive or transmit and receive. As is well known to those skilled inthe art, a wireless terminal is also commonly called a cell phone, apager, a wireless transmit/receive unit (WTRU), a user equipment (UE), amobile station, wireless handset, a fixed or mobile subscriber unit, apager, a cellular telephone, a personal digital assistant (PDA), anInternet of Things (IoT) device, a computer, and any other type ofdevice capable of operating in a wireless environment are examples ofwireless terminals.

DETAILED DESCRIPTION

Telecommunications System 100—FIG. 1 depicts a diagram of the salientcomponents of telecommunications system 100 in accordance with theillustrative embodiment of the present invention. Telecommunicationssystem 100 comprises: wireless terminal 101, cellular base stations103-1, 103-2, and 103-3, Wi-Fi base stations 104-1 and 104-2, wirelessinfrastructure 111, location-based application server 112, locationengine 113, airport pressure station 114, and a Global NavigationSatellite System (GNSS) that includes Global Positioning System (GPS)constellation 131, interrelated as shown.

Wireless infrastructure 111, location-based application server 112,location engine 113, and Wi-Fi base stations 104-1 and 104-2 are allconnected to one or more interconnected computer networks (e.g., theInternet, a local-area network, a wide-area network, etc.) and, as such,can exchange data in well-known fashion.

Wireless terminal 101 is a device that provides bi-directional voice,data, and video telecommunications services to its user (not shown).Terminal 101 also performs the processes described below and in theaccompanying figures, including measuring temperature and barometricpressure, and providing temperature and pressure measurements. Terminal101 comprises the hardware and software necessary to do theaforementioned tasks. Furthermore, wireless terminal 101 is mobile andcan be at any location within geographic region 120 at any time.

Wireless terminal 101 provides the aforementioned telecommunicationsservices to their respective users and perform the aforementioned tasks.It will, however, be clear to those skilled in the art, after readingthis disclosure, how to make and use embodiments of the presentinvention in which wireless terminal 101 provides a different set ofservices or perform a different set of tasks.

In accordance with the illustrative embodiment, in order to supportlocation estimation, wireless terminal 101 can receive one or more radiosignals from each of base stations 103-1, 103-2, and 103-3, Wi-Fi basestations 104-1 and 104-2, and GPS constellation 131, in well-knownfashion. Wireless terminal 101 is also capable of identifying each radiosignal it receives, in well-known fashion, and of transmitting theidentity of each signal it receives to location engine 113. The wirelessterminals are further capable of measuring one or morelocation-dependent traits (e.g., amplitude, phase, etc.) of each radiosignal they receive, in well-known fashion, and of transmitting eachmeasurement they generate to location engine 113. As those who areskilled in the art will appreciate after reading this specification,wireless terminal 101 can use and/or support one or more technologiesother than WiFi and GPS for estimating the location of the wirelessterminal.

In accordance with the illustrative embodiment, wireless terminal 101can transmit one or more radio signals—that can be received by one ormore of base stations 103-1, 103-2, and 103-3 and Wi-Fi base stations104-1 and 104-2—in accordance with specific parameters (e.g., MACaddress, signal strength, frequency, coding, modulation, band, etc.), inwell-known fashion, and of transmitting those parameters to locationengine 113.

In accordance with the illustrative embodiment, and as described indetail below, wireless terminal 101 comprises a barometer (shown in FIG.2 as barometer 205). Accordingly, wireless terminal 101 is capable ofmeasuring (e.g., periodically, sporadically, and on-demand) thetemperature and barometric pressure, in well-known fashion, and oftransmitting the measurements to location engine 113.

Although the illustrative embodiment depicts telecommunications system100 as comprising one wireless terminal, it will be clear to thoseskilled in the art, after reading this disclosure, how to make and usealternative embodiments of the present invention that comprise anynumber of wireless terminals.

Cellular base stations 103-1, 103-2, and 103-3 communicate with wirelessinfrastructure 111 via wireline or wireless backhaul and with wirelessterminal 101 via radio in well-known fashion. As is well known to thoseskilled in the art, base stations are also commonly referred to by avariety of alternative names such as access points, nodes, networkinterfaces, etc. Although the illustrative embodiment comprises threecellular base stations, it will be clear to those skilled in the art,after reading this disclosure, how to make and use alternativeembodiments of the present invention that comprise any number ofcellular base stations.

In accordance with the illustrative embodiment of the present invention,cellular base stations 103-1, 103-2, and 103-3 are terrestrial andimmobile, and base station 103-3 is situated within geographic region120. It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which some or all of the base stations are airborne,marine-based, or space-based, regardless of whether or not they aremoving relative to the Earth's surface, and regardless of whether or notthey are within geographic region 120.

Cellular base stations 103-1, 103-2, and 103-3 comprise the hardware andsoftware necessary to be Long-Term Evolution (LTE) 3GPP-compliant andperform the processes described below and in the accompanying figures.In some alternative embodiments of the present invention, base stations103-1, 103-2, and 103-3 communicate in accordance with a differentcellular standard. Each of cellular base stations 103-1, 103-2, and103-3 are capable of continually, for example and without limitation:

-   -   a. receiving one or more radio signals transmitted by wireless        terminal 101, and    -   b. identifying each radio signal transmitted by wireless        terminal 101, in well-known fashion, and of transmitting the        identity of those signals to location engine 113, and    -   c. measuring one or more location-dependent traits of each radio        signal transmitted by wireless terminal 101, in well-known        fashion, and of transmitting the measurements to location engine        113, and    -   d. transmitting one or more signals to wireless terminal 101 in        accordance with specific parameters (e.g., signal strength,        frequency, coding, modulation, etc.), in well-known fashion, and        of transmitting those parameters to location engine 113, and    -   e. broadcasting one or more signals that wireless terminals can        use for various purposes (e.g., mobile assisted handoff,        location determination, etc.).        It will be clear to those skilled in the art how to make and use        cellular base stations 103-1, 103-2, and 103-3.

Wi-Fi base stations 104-1 and 104-2 communicate with wireless terminal101 via radio in well-known fashion and in accordance with a WiFiprotocol. In some alternative embodiments of the present invention, basestations 104-1 and 104-2 communicate in accordance with a different IEEE802.11 standard or wireless LAN standard entirely. Wi-Fi base stations104-1 and 104-2 are terrestrial, immobile, and within geographic region120. Although the illustrative embodiment comprises two Wi-Fi basestations, it will be clear to those skilled in the art, after readingthis disclosure, how to make and use alternative embodiments of thepresent invention that comprise any number of Wi-Fi base stations.

Each of Wi-Fi base stations 104-1 and 104-2 are capable of continually:

-   -   a. receiving one or more radio signals transmitted by wireless        terminal 101, and    -   b. identifying each radio signal transmitted by wireless        terminal 101, in well-known fashion, and of transmitting the        identity of those signals to location engine 113, and    -   c. measuring one or more location-dependent traits of each radio        signal transmitted by wireless terminal 101, in well-known        fashion, and of transmitting the measurements to location engine        113, and    -   d. transmitting one or more signals to wireless terminal 101 in        accordance with specific parameters (e.g., signal strength,        frequency, coding, modulation, etc.), in well-known fashion, and        of transmitting those parameters to location engine 113, and    -   e. broadcasting one or more signals that wireless terminals can        use for various purposes (e.g., mobile assisted handoff,        location determination, etc.).

It will be clear to those skilled in the art how to make and use Wi-Fibase stations 104-1 and 104-2.

Wireless infrastructure 111 comprises a switch that orchestrates theprovisioning of telecommunications service to wireless terminal 101 andthe flow of information to and from location engine 113, as describedbelow and in the accompanying figures. As is well known to those skilledin the art, wireless switches are also commonly referred to by othernames such as mobile switching centers, mobile telephone switchingoffices, routers, and so on.

Location-based application server 112 comprises hardware and softwarethat uses the estimate of the location of wireless terminal101—generated by location engine 113—in a location-based application, inwell-known fashion. Location-based applications are well-known in theart and provide services such as without limitation E-911 routing,navigation, location-based advertising, weather alerts. In accordancewith the illustrative embodiment, location-based application server 112is implemented on a data-processing system made up of one or more servercomputers.

Location engine 113 is a data processing system that comprises hardwareand software that generates one or more estimates of the locations ofwireless terminal 101 as described below and in the accompanyingfigures. Location engine 113 maintains one or more databases (e.g.,geographic information system [GIS] database, etc.) which are describedin detail below. In accordance with the illustrative embodiment,location engine 113 is implemented on a data-processing system made upof one or more server computers. It will be clear to those skilled inthe art, after reading this disclosure, how to make and use locationengine 113.

Location engine 113 is depicted in FIG. 1 as physically distinct fromwireless infrastructure 111. However, it will be clear to those skilledin the art, after reading this disclosure, how to make and usealternative embodiments of the present invention in which locationengine 113 is wholly or partially integrated into wirelessinfrastructure 111.

Airport pressure station 114, which is a first pressure reference,comprises hardware and software that continually measures the outdoortemperature (i.e., provides a measurement of temperature representativeof an outdoor location) and measures the atmospheric pressure (i.e.,provides a measurement of barometric pressure representative of anoutdoor location), in well-known fashion, and transmits thosemeasurements to a central location that is accessible by location engine113 (e.g., a National Weather Service database, etc.). In measuringtemperature and barometric pressure at an outdoor location, airportpressure station 114 is not subject to any stack effect. Station 114 isat a known lateral location in geographic region 120.

In some embodiments of the present invention, airport pressure station114 provides measurements of temperature and/or barometric pressurerepresentative of a known outdoor location by taking the measurements ata well-ventilated indoor location (e.g., a ventilated shelter, etc.), orby taking pressure measurements at an indoor location at which thepressure is equal to the outdoor pressure at the same elevation.

In accordance with the illustrative embodiment, airport pressure station114 is situated at an airport (i.e., is on the airport's premises) andserves the airport. In some embodiments of the present invention,station 114 is at a weather-reporting station, while in otherembodiments station 114 is at a different type of station (i.e., neitherat an airport nor reporting the weather). Although the illustrativeembodiment comprises only one airport pressure station, it will be clearto those skilled in the art how to make and use alternative embodimentsof the present invention that comprise any number of airport pressurestations.

The illustrative embodiment depicts telecommunications system 100 ascomprising one airport pressure station. However, it will be clear tothose skilled in the art, after reading this disclosure, how to make anduse alternative embodiments of the present invention that comprise anynumber of airport pressure stations.

Wireless Terminal 101—FIG. 2 depicts a block diagram of the salientcomponents of wireless terminal 101 in accordance with the illustrativeembodiment of the present invention. Wireless terminal 101 comprises:radio receiver and transmitter 201, processor 202, memory 203, GPSreceiver 204, barometer 205, and human interface 207, interconnected asshown. The block diagram depicted in FIG. 2 can also be consideredrepresentative of other wireless terminals.

Radio receiver and transmitter component 201 comprises hardware andsoftware that enables wireless terminal 101 to receive (and analyze)radio signals and to transmit radio signals. In accordance with theillustrative embodiment, wireless telecommunications service is providedto wireless terminal 101 in accordance with both the Long-Term Evolution(LTE) 4G air-interface standard of the 3^(rd) Generation PartnershipProject (“3GPP”) and the WiFi standard. After reading this disclosure,however, it will be clear to those skilled in the art how to make anduse alternative embodiments of the present invention that operate inaccordance with one or more other air-interface standards (e.g., a 5G orother standard under development, a different 4G standard, Global SystemMobile “GSM,” UMTS, CDMA-2000, IS-136 TDMA, IS-95 CDMA, 3G WidebandCDMA, other IEEE 802.11 or wireless LAN standard, 802.16 WiMax,Bluetooth, etc.) in one or more frequency bands. It will be clear tothose skilled in the art how to make and use radio receiver andtransmitter 201.

Processor 202 is hardware under the command of software stored in memory203 that performs all of the relevant functions described below and inthe accompanying figures. It will be clear to those skilled in the arthow to make and use processor 202.

Memory 203 is a non-transitory, non-volatile random-access memory thatholds all of the programming and data required for the operation ofwireless terminal 101, and includes operating system 211, applicationsoftware 212, and database 213. It will be clear to those skilled in theart how to make and use memory 203.

GPS receiver 204 is hardware and software that enables wireless terminal101 to determine its own location. GPS receiver 204 interacts with GPSsatellites in constellation 131. It will be clear to those skilled inthe art how to make and use GPS receiver 204.

Barometer 205 is a barometric sensor device and typically comprises ahardware MEMS sensor that measures the atmospheric pressure at wirelessterminal 101, thereby providing barometric pressure measurements. Inaccordance with the illustrative embodiment, barometer 205 comprises theLSP331AP MEMS pressure sensor from ST Microelectronics and/or the BoschBMP280 sensor, but it will be clear those skilled in the art, afterreading this disclosure, how to make and use alternative embodiments ofthe present invention that use a different sensor to measure theatmospheric pressure.

mom Thermometer 206 is a hardware temperature sensor that measures theambient temperature at wireless terminal 101. In accordance with theillustrative embodiment, thermometer 206 comprises the Bosch BMP280sensor, which also measures temperature in addition to pressure, but itwill be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention that use a different sensor to measure the ambient temperatureat wireless terminal 101. For example, the ADT7420 temperature sensorfrom Analog Devices is capable of measuring temperature. In someembodiments of the present invention, wireless terminal 101 has nothermometer, in which case the system disclosed herein can determineindoor temperature through other means as described below.

Human interface 207 is hardware and software that enables a person tointeract with wireless terminal 101. Human interface 207 comprises adisplay, keypad, microphone, and speaker. It will be clear to thoseskilled in the art how to make and use human interface 207.

Wireless terminal 101 can perform at least some of the processesdescribed below and in the accompanying figures. For example and withoutlimitation, wireless terminal 101 is capable of:

-   -   a. receiving one or more radio signals transmitted by cellular        base stations 103-1, 103-2, and 103-3, Wi-Fi base stations 104-1        and 104-2, and GPS constellation 131, and    -   b. identifying each radio signal transmitted by cellular base        stations 103-1, 103-2, and 103-3, Wi-Fi base stations 104-1 and        104-2, and GPS constellation 131, in well-known fashion, and of        transmitting the identity of those signals, or information        related to the identity of those signals, to location engine        113, and    -   c. measuring one or more location-dependent traits of each radio        signal transmitted by cellular base stations 103-1, 103-2, and        103-3, Wi-Fi base stations 104-1 and 104-2, and GPS        constellation 131, in well-known fashion, and of transmitting        the measurements to location engine 113, and    -   d. transmitting one or more signals to cellular base stations        103-1, 103-2, and 103-3, Wi-Fi base stations 104-1 and 104-2 in        accordance with specific parameters (e.g., signal strength,        frequency, coding, modulation, etc.), in well-known fashion, and        of transmitting those parameters to location engine 113, and    -   e. measuring the temperature and barometric pressure at wireless        terminal 101, in well-known fashion, and transmitting those        measurements to location engine 113. In some embodiments of the        present invention, wireless terminal can measure the temperature        at wireless terminal 101, in well-known fashion, and transmit        those measurements to location engine 113.        It will be clear to those skilled in the art how to make and use        wireless terminal 101.

Location engine 113—FIG. 3 depicts a block diagram of the salientcomponents of location engine 113 in accordance with the illustrativeembodiment. Location engine 113 comprises: receiver and transmitter 301,processor 302, and memory 303, which are interconnected as shown.

Receiver and transmitter component 301 enables location engine 113 totransmit to and receive from wireless terminal 101, wirelessinfrastructure 111, location-based application server 112, and airportpressure station 114. It will be clear to those skilled in the art howto make and use receiver and transmitter 301.

Processor 302 is a general-purpose processor that can execute anoperating system, the application software that performs operations 401through 411 (described herein and shown in FIG. 4), and of populating,amending, using, and managing a GIS database, as described in detailbelow and in the accompanying figures. It will be clear to those skilledin the art how to make and use processor 302.

In general, the GIS database contains information for geographic region120, including without limitation, the physical characteristics of allof the structures in geographic region 120. It will be clear to thoseskilled in the art, after reading this specification, how to make anduse the GIS database.

Memory 303 is a non-transitory, non-volatile memory that stores:

-   -   a. operating system 311, and    -   b. application software 312, and    -   c. the GIS database in database 313.        In some embodiments of the present invention, memory 303 is in        the form of cloud storage or network storage. In any event, it        will be clear to those skilled in the art how to make and use        memory 303.

Operation of the Illustrative Embodiment—FIG. 4 depicts a flowchart ofthe salient processes performed as part of method 400 in accordance withthe illustrative embodiment of the present invention. It will be clearto those having ordinary skill in the art, after reading the presentdisclosure, how to make and use alternative embodiments of method 400,as well as the other methods disclosed in this specification, whereinthe recited operations sub-operations, and messages are differentlysequenced, grouped, or sub-divided—all within the scope of the presentdisclosure. It will also be clear to those skilled in the art, afterreading the present disclosure, how to make and use alternativeembodiments of the disclosed methods wherein some of the describedoperations, sub-operations, and messages are optional, or are omitted.

It will also be clear to those skilled in the art, after reading thepresent disclosure, how to make and use alternative embodiments of thedisclosed methods wherein some of the disclosed operations are performedby other elements and/or systems. For example and without limitation, atleast some of the operations disclosed as being performed by locationengine 113 can be performed by one or more wireless terminals (e.g.,terminal 101, etc.).

In accordance with operation 401, the GIS database is initialized andstored in memory 303 of location engine 113. Operation 401 is describedin detail below and in regard to FIG. 5.

In accordance with operation 403, location engine 113 calibrates thebarometric pressure sensor of wireless terminal 101, resulting in anestimate of the measurement bias of the sensor. Operation 403 isdescribed below and in regard to FIG. 9.

In accordance with operation 405, location engine 113 obtains anestimate of the lateral location of wireless terminal 101, as generatedby wireless terminal 101 (e.g., via Global Navigation Satellite System[GNSS], GPS, etc.). In some embodiments of the present invention,location engine 113 itself generates an estimate of the lateral locationof wireless terminal 101, with or without the lateral location providedby wireless terminal 101 being used, based on:

-   -   a. the location-dependent information conveyed by a radio signal        exchanged between a base station (e.g., cellular base station        103-i, Wi-Fi base station 104-j, etc.) and wireless terminal 101        (e.g., the empirical data for received radio signals, etc.), and    -   b. a location-trait database,        in well-known fashion.

As those who are skilled in the art will appreciate after reading thisspecification, in some other alternative embodiments the laterallocation can be determined using a different technique than thosedescribed above (e.g., WiFi, Bluetooth, OTDOA, etc.). Moreover, as thosewho are skilled in the art will appreciate after reading thisspecification, more than one technique can be combined in order todetermine the lateral location, in some embodiments of the presentinvention.

In accordance with operation 407, location engine 113 collectsmeasurements of barometric pressure from airport pressure station 114(i.e., either directly or indirectly) and wireless terminal 101. In someembodiments of the present invention, location engine 113 collectsmeasurements of barometric pressure from other airport pressure stationsas well, or from other wireless terminals as well, or both. In someembodiments of the present invention, location engine 113 can alsocollect measurements of temperature. Operation 407 is described indetail below and in regard to FIG. 17.

In accordance with operation 409, location engine 113 generates anestimate of the elevation of wireless terminal 101 based on:

-   -   a. the estimate of lateral location of wireless terminal 101        received or generated in accordance with operation 405,    -   b. a measurement of barometric pressure at pressure reference        114 obtained in accordance with operation 407,    -   c. a measurement of barometric pressure at wireless terminal 101        obtained in accordance with operation 407, and    -   d. an estimate of bias obtained in accordance with operation        403.        Operation 409 is described in detail below and in regard to FIG.        18.

In accordance with operation 411, location engine 113 transmits:

-   -   a. the estimate of the lateral location of wireless terminal 101        generated in accordance with operation 405, and/or    -   b. the estimate of the elevation of wireless terminal 101        generated in accordance with operation 409, and/or    -   c. the estimate of the measurement bias of wireless terminal 101        generated in accordance with operation 403, and/or    -   d. one or more defining characteristics of the new-measurement        distribution generated in accordance with operation 1001, and/or    -   e. one or more defining characteristics of the updated        probability distribution generated in accordance with operation        1005, and/or    -   f. any other information used to determine the lateral location,        estimate of elevation, and/or measurement bias,        to location-based application server 112 and/or to wireless        terminal 101 for use in a location-based application and/or to        yet another data-processing system (e.g., server computer,        wireless terminal, etc.).

In some embodiments of the present invention, location engine 113displays (e.g., on a display, etc.) information related to the estimateof lateral location and/or estimate of elevation, instead of or inaddition to transmitting them. In any event, it will be clear to thoseskilled in the art how to make and use embodiments of the presentinvention that perform operation 411.

After operation 411 is completed, control passes back to operation 403.

Operation 401: Construct the GIS Database—FIG. 5 depicts a flowchart ofthe salient processes performed in accordance with operation 401.

At operation 501, the GIS database is constructed and stored in memory303 of location engine 113. As part of operation 501, geographic region120 is delimited and surveyed. The GIS database represents thegeographic region within which wireless terminal might be present andwhose location can be estimated.

In accordance with the illustrative embodiment, geographic region 120comprises approximately four city blocks of an urban environment. Itwill be clear to those skilled in the art however, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which geographic region 120 has any area of any shape andany population density and development.

As part of operation 501, a detailed map of the ground level ofgeographic region 120 is made in well-known fashion, and as shown inFIG. 6. The elements within region 120 as depicted as not necessarilydrawn to scale geographically. For example, airport pressure station 114is depicted as being relatively close to the cluster of buildings inorder to both fit all of the described elements within the same figureand provide sufficient detail for each element.

FIG. 7 depicts an isometric drawing of a portion of geographic region120, which spans approximately four city blocks and comprises, amongother elements, park 601, boxy building 602, empty lot 603, cylindricalbuilding 604, and airport pressure station 114. It will be clear tothose skilled in the art, after reading this disclosure, how to make anduse alternative embodiments of the present invention that comprise anyarea, any geographic features, and any number, size, height, and shapeof structures, such as buildings 602 and 604.

In accordance with the illustrative embodiment, as part of operation501, the coordinate positions of the various features of one or moreobjects (e.g., buildings, structures, etc.) in geographic region 120 aredetermined and stored in the GIS database. The positions of one or morefeatures of the objects can be determined by referencing thethree-dimensional survey of geographic region 120, which is depicted inFIG. 8.

As described above, buildings 602 and 604 are represented withcoordinates. As those who are skilled in the art will appreciate afterreading this specification, in some embodiments of the present inventionbuildings 602 and 604, and objects in general, can be represented in adifferent way, such as by using a vector-based approach. For example andwithout limitation, one or more of the buildings in a geographic areacan be described by a polygon shape of a building footprint, or rooftop,and the height of the building. Furthermore, any comparisons of distancecan be made based on the polygon shape and/or polygon height stored,versus the coordinates stored.

Operation 403: Calibrate the Barometric Sensor of Wireless Terminal101—FIG. 9 depicts a flowchart of the salient processes performed inaccordance with operation 403.

In accordance with operation 901, location engine 113 obtains anestimate of the lateral location of wireless terminal 101. Operation 901is similar to operation 405 described above and in regard to FIG. 4. Theestimate of location comprises i) geographical coordinates of thelocation and ii) an uncertainty or uncertainties in the geographicalcoordinates of the estimate of location.

In accordance with the illustrative embodiment of the present invention,the first estimate of the location of wireless terminal 101 comprises aset of geographical coordinates representing the latitude/longitude(“lat/lon”) of the wireless terminal. Latitude represents location alonga first dimension (i.e., “north-south”), and longitude representslocation along a second dimension (i.e., “east-west”).

In some embodiments of the present invention, the first estimate of thelocation of wireless terminal 101 also comprises values for theuncertainties in one or more components of the location estimate (e.g.,an uncertainty in latitude, an uncertainty in longitude, an overalluncertainty, etc.). The horizontal uncertainty is based on theunderlying lateral location estimation technique that results in lat/loncoordinates. In general, the uncertainty can be expressed in terms of aconfidence level, a distance given a particular confidence level, or adifferent well-known metric.

In accordance with operation 903, location engine 113 collectsmeasurements of barometric pressure from airport pressure station 114(i.e., either directly or indirectly) and wireless terminal 101.Operation 903 is similar to operation 407 described below and in regardto FIG. 17.

In accordance with operation 905, location engine 113 generates anupdated probability distribution of the bias of pressure sensor 205 inwireless terminal 101. The updated probability distribution is definedby i) an updated lower bound of pressure bias, ii) a correspondinglower-bound uncertainty, iii) an updated upper bound of pressure bias,and iv) a corresponding upper-bound uncertainty. The updated probabilitydistribution is based on i) the measurements of barometric pressure frompressure station 114 and wireless terminal 101 collected in accordancewith operation 903, and ii) the geographical coordinates for the laterallocation and the uncertainty obtained in accordance with operation 901,as well as iii) a previously-updated probability distribution, ifavailable. Operation 905 is described below and in regard to FIG. 10.

In accordance with operation 907, location engine 113 determines anupdated estimate of measurement bias based on the updated probabilitydistribution of pressure bias determined in accordance with operation905. Operation 907 is described below and in regard to FIG. 16.

After operation 907, control of task execution proceeds to operation405.

Operation 905: Generate a Probability Distribution of Pressure Bias—FIG.10 depicts a flowchart of the salient processes performed in accordancewith operation 905.

In accordance with operation 1001, location engine 113 generates anew-measurement probability distribution based on one or more newlocation measurements and/or pressure measurements. In some embodimentsof the present invention, the distribution is characterized as having aflat top, with exponentially decaying sides. The distribution can bedefined by four parameters: a low endpoint and a high endpoint, whichdefine the interval of the flat top, as well as a lower uncertainty andan upper uncertainty, which define the average decay length of each ofthe exponential sides adjacent to the respective low endpoint and highendpoint. For pedagogical purposes, such a distribution is referred toin this specification as a “low/high distribution.” FIG. 15A shows anexample of new-measurement probability distribution 1500, described indetail below. Operation 1001 itself is described below and in regard toFIG. 11.

In accordance with operation 1003, location engine 113 determineswhether or not a previous probability distribution is available—that is,a probability distribution generated prior to new-measurementprobability distribution 1500. If a previous distribution isavailable—that is, from a prior iteration of operation 905—then controlof execution proceeds to operation 1005. Otherwise, new-measurementdistribution 1500 is used as the updated distribution in operation 907and control passes to operation 907.

In accordance with operation 1005, location engine 113 generates anupdated probability distribution by combining mathematically i)new-measurement probability distribution 1500 and ii) thepreviously-generated probability distribution.

A general approach of combining the two probability distributions is nowdescribed. Already stored in memory from a previous iteration ofoperation 905 is a previously-generated low/high distribution thatdescribes the current knowledge about the pressure sensor bias. Inaccordance with operation 1001, location engine 113 generates a resultthat also provides bias information, and is also encoded as a low/highdistribution. To update the probability distribution in accordance withoperation 1003, location engine 113 multiplies the two low/highprobability distributions and renormalizes the product into a resultingprobability distribution. The resulting probability distribution is nota true low/high distribution, as defined earlier, so location engine 113approximates a low/high distribution that best fits the resultingprobability distribution.

In order to understand how location engine 113 approximates a low/highdistribution, it is important to understand the limiting case in whichthere are only perfect uniform distributions being generated, wherein aperfect uniform distribution between the low and high endpoint has lowand high uncertainties of zero. If location engine 113 were to multiplyand renormalize two uniform distributions, the resulting distributionwould be another uniform distribution whose interval is the intersectionof the two. In that case, as location engine 113 receives moremeasurements, the intersection becomes smaller and smaller, thusresembling convergence.

The problem, however, is when the intervals do not overlap, in whichcase the resulting probability distribution is undefined. The underlyingcause is that the real distribution does not suddenly drop off to zero.This is a main reason why location engine 113 uses a low/highdistribution (i.e., with low/high uncertainties), in contrast to auniform distribution (i.e., without low/high uncertainties), inaccordance with the illustrative embodiment.

There are advantages to using the low/high distribution of theillustrative embodiment. First, as with the uniform distribution, due toits flat top, the low/high probability distribution is robust to thelack of independence between measurements. In particular, processingthat involves a distribution with a flat top will not suddenly decreasethe uncertainty from a large number of high-uncertainty measurements, asprocessing involving a Gaussian-like distribution would (i.e., with apeaked top). Second, unlike the uniform distribution, the low/highdistribution elegantly and reasonably handles the case when the low/highinterval of the new-measurement probability distribution and thelow/high interval of the previously-generated probability distributiondo not have a common intersection.

Operation 1005 is described in detail below and in regard to FIG. 14.

Operation 1001: Generate a New-Measurement Probability Distribution ofPressure Bias—FIG. 11 depicts a flowchart of the salient processesperformed in accordance with operation 1001, in which location engine113 generates new-measurement probability distribution 1500 based on oneor more new measurements having been received by the location engine.For example, location engine 113 can receive geographical coordinatesthat describe the lateral location of wireless terminal 101 and/or anuncertainty in the lateral location of the wireless terminal, any ofwhich can trigger operation 1001 or can be used in generating thenew-measurement probability distribution. As those who are skilled inthe art will appreciate, after reading this specification, locationengine 113 can generate new-measurement probability distribution 1500,as well as apply distribution 1500 later on in order to update thecurrent probability distribution at operation 1005, based on Bayesianinference or a different suitable method.

In accordance with operation 1101, location engine 113 generates datapoints from the geographical coordinates and/or the location uncertaintyobtained in accordance with operation 901. The data points are membersof a nonempty set of data points in space and, in some embodiments, areconfined initially to a horizontal plane. The location engine generatesthe data points based on one or more probability distributions definedby at least one of i) the one or more geographical coordinates and ii)the uncertainty or uncertainties in the one or more geographicalcoordinates that are part of the estimate of location generated inaccordance with operation 901. Location engine 113 generates the datapoints based on i) a first probability distribution that is defined by afirst geographic coordinate value along a first dimension (e.g., x-axis,etc.), and/or ii) a second normal distribution that is defined by asecond geographic coordinate value along a second dimension (e.g.,y-axis, etc.), wherein the geographic coordinates are part of theestimate of location. The data points generated are represented bycoordinate values along the represented dimensions.

In accordance with the illustrative embodiment, location engine 113applies a normal (or Gaussian) distribution, or an approximationthereof, as the probability distribution along one or more dimensions ofthe nonempty set of data points. In some embodiments of the presentinvention, the nonempty set of data points in space is a “point cloud”or “pixel cloud,” as is known in the art.

In some embodiments of the present invention, the center of the set ofdata points coincides with, or at least is based on, one or more of thelatitude and the longitude provided in the estimate of location ofwireless terminal 101 obtained at operation 901, in any combination. Insome embodiments, the first geographic coordinate value defines the meanof the first probability distribution and/or the second geographiccoordinate value defines the mean of the second probabilitydistribution.

In some embodiments of the present invention, a horizontal component ofthe uncertainty (i.e., in the one or more geographical coordinates ofthe first estimate), H_(unc), defines the standard deviation of aprobability distribution along a horizontal dimension.

Location engine 113 generates M data points, in the form of lateralcoordinate values, for the set of data points in space. The m^(th) datapoint (P_(mx), P_(my)) in the set of data points, for m equals 1 throughM, is based on the following equations:

P _(mx) =N _(m)(X, H _(unc))   (Eq. 2)

P _(my) =N _(m)(Y, H _(unc))   (Eq. 3)

wherein:

-   -   (X, Y) represents the geographical coordinates of latitude and        longitude, respectively, of the estimate of location of wireless        terminal 101,    -   H_(unc) represents the horizontal (lateral) uncertainty across        latitude and longitude,    -   N_(m)(μ, σ) is a random variable of normal distribution with        mean μ and standard deviation σ, generated for data point m.

Put differently, for all M data points (P_(mx), P_(my)), the set ofP_(mx) values is characterized by a first probability distribution, andthe set of P_(my) values is characterized by a second probabilitydistribution, which might or might not be the same as the firstprobability distribution.

Location engine 113 generates M data points total, as described above,wherein the value of M can be selected to achieve an accuracy to adesired number of significant digits. For example, the value of M can beequal to 100. In some embodiments of the present invention, the numberof data points M can be based on the estimation uncertainty or on theenvironment, or both. For example, a greater uncertainty might dictategenerating more data points, while a lesser uncertainty might dictategenerating fewer data points.

In accordance with operation 1103, location engine 113 determines, interms of elevation of the corresponding geographical coordinates, thelowest data point and the highest data point in the set of M data pointsgenerated in accordance with operation 1101. In some embodiments of thepresent invention, these points correspond to the lowest and highestelevations at which wireless terminal 101 can be present (e.g., at thetop of a building, at the bottom of a building, on or near ground levelbut not in high up and in mid-air, etc.). The elevation that correspondsto the coordinates of each data point can be obtained from the GISdatabase constructed in accordance with operation 501. In the GISdatabase, the terrain data includes elevation data obtained previously(e.g., by sampling the terrain surface, etc.) and the building dataincludes building height data (i.e., the highest points of the building)and depth data (i.e., the lowest points of the building) obtainedpreviously (e.g., by relying on building construction specifications,etc.).

FIGS. 12A and 12B depicts a first example of the data points generatedin accordance with operations 1101 and 1103, and corresponding to theestimated location of wireless terminal 101 at time t₁ determined inaccordance with operation 901. FIG. 12A depicts a top view of a portionof geographic region 120, including buildings 602 and 604 and the areain the vicinity of the buildings. FIG. 12B depicts an elevation view ofa slice, along line 1203, of what is depicted in FIG. 12A.

FIGS. 12A and 12B also depict at least some of the data points that makeup point cloud 1201, which comprises the data points generated inaccordance with operation 1101. Some of the data points in point cloud1201 are data points 1201-1, 1201-2, and 1201-3. The position of each ofthe data points within point cloud 1201 is marked with an “X”. Forreasons of clarity, point cloud 1201 is depicted as a circle having aradius defined by the position of the data point furthest away fromcenter of the circle, namely data point 1201-3, although the data pointsthemselves exist in memory as discrete points and correspond togeographical coordinates. The larger the circle, the greater theuncertainty in the estimate of location; the smaller the circle, thelesser the uncertainty in the estimate of location. The coordinates ofthe discrete data points coexist with the coordinates of the variousfeatures stored in the GIS database, such as features associated withbuildings 602 and 604 and terrain-related features.

Point cloud 1201 is centered around the estimate of the location ofwireless terminal 101 at time t₁, obtained in accordance with operation901. As depicted, the estimate of location at time t₁ has wirelessterminal 101 in the vicinity of building 602. In regard to the highestdata point within point cloud 1201, location engine 113 determines thatdata point 1202-1, coinciding with building 602, is at a laterallocation having the highest elevation—that is, at the top of thebuilding. In regard to the lowest data point, although data point 1202-2is at a lateral location having the lowest terrain elevation, data point1202-1 is at a lateral location having the lowest elevation overall—thatis, in the basement of the building and lower than at any point in thenearby terrain, including at data point 1202-2.

As mentioned earlier, FIG. 12B is an elevation view along line 1203,which is defined by data points 1202-1 and 1202-2. FIG. 12B includesdata point 1202-1—now split into highest point 1202-1 a and lowest point1202-1 b—and data point 1202-2. Although data point 1202-2 is the lowestpoint in the terrain, it is not as low as data point 1202-1 b, thelowest point overall.

FIGS. 13A and 13B depict a second example of the data points generatedin accordance with operations 1101 and 1103, and corresponding to theestimated location of wireless terminal 101 at time t₂ determined inaccordance with operation 901. FIG. 13A depicts a top view of a portionof geographic region 120, including buildings 602 and 604 and the areain the vicinity of the buildings. FIG. 13B depicts an elevation view ofa slice, along line 1303 defined by points 1301-1 and 1301-2, of what isdepicted in FIG. 13A.

FIGS. 13A and 13B also depict at least some of the data points that makeup point cloud 1301, which comprises the data points generated inaccordance with operation 1101. Some of the data points in point cloud1301 are data points 1301-1, 1301-2, and 1301-3. The position of each ofthe data points within point cloud 1301 is marked with an “X”. Pointcloud 1301 is depicted as a circle having a radius defined by theposition of the data point furthest away from center of the circle,namely data point 1301-3.

Point cloud 1301 is centered around the estimate of the location ofwireless terminal 101 at time t₂, obtained in accordance with operation901. As depicted, the estimate of location at time t₂ has wirelessterminal 101 in the vicinity of building 604. Each of points 1301-1 and1301-2 are candidates for both the lowest point and highest point withinpoint cloud 1301 and, as such, are split into points 1301-1 a and 1301-1b and points 1302-1 a and 1302-1 b, respectively. In regard to thehighest data point within point cloud 1301, location engine 113determines that data point 1302-1 a, coinciding with building 604, is ata lateral location having the highest elevation—that is, at the top ofthe building. In regard to the lowest data point, although data point1302-1 b coincides with the basement of building 604, data point 1302-2b is at a lateral location having the lowest elevation overall—that is,at the bottom of subway tunnel 1304.

In accordance with operation 1105, location engine 113 determines theatmospheric pressures for the lowest data point and the highest datapoint determined in accordance with operation 1103. Location engine 113uses a barometric pressure measurement at airport pressure station 114and, knowing the elevation of pressure station 114 with respect to aparticular reference level (e.g. mean sea level, etc.), scales thepressure measurement up or down to the lowest data point and to thehighest data point. This results respectively in a highest possiblepressure and a lowest possible pressure, recognizing that atmosphericpressure is inversely related to elevation. Bias-adjusted pressure ofwireless terminal 101 can be expected to fall within the range of thehighest and lowest possible pressures.

In accordance with operation 1107, location engine 113 determines alower bound and an upper bound of pressure bias for the current set ofdata. Engine 113 determines the lower bound of pressure bias based on i)the barometric pressure received from wireless terminal 101 inaccordance with operation 903, minus ii) the highest possible pressure(i.e., at the lowest-elevation data point) determined in accordance withoperation 1105. Engine 113 determines the upper bound of pressure biasbased on i) the barometric pressure received from wireless terminal 101in accordance with operation 903, minus ii) the lowest possible pressure(i.e., at the highest-elevation data point) determined in accordancewith operation 1105.

In accordance with operation 1109, location engine 113 determines alower uncertainty associated with the lower bound determined inaccordance with operation 1107 and an upper uncertainty associated withthe upper bound determined in accordance with operation 1107. The lowerand upper uncertainties describe the average decay length of each of theexponential sides of the low/high distribution, in some embodiments ofthe present invention.

There are various reasons why these uncertainties exist, and thecalculation of the lower and upper uncertainties is based on anunderstanding of the reasons. A first reason is that the GIS data (e.g.,terrain, building features, etc.) that is being used to determine upperand lower bounds of pressure bias might be inaccurate or in error. Forexample, the building data (e.g., building height, basement depth, etc.)might only be guaranteed to a certain accuracy. A second reason is thata weather station reference is used to convert elevation to pressurebiases, and the weather station reference itself can introduceuncertainties. A third reason is that the lat-lon uncertainties thereare used to generate the data points in operation 1101 can introduceuncertainty in the lower bound and upper bound of the pressure bias.

In accordance with operation 1111, location engine 113 stores anew-measurement probability distribution defined by the lower bound,upper bound, lower bound uncertainty, and upper bound uncertainty.

Control of task execution then passes to operation 1003.

Operation 1005: Generate an Updated Probability Distribution of PressureMeasurement Bias—FIG. 14 depicts a flowchart of the salient processesperformed in accordance with operation 1005 for generating an updatedprobability distribution of pressure measurement bias.

FIGS. 15A, 15B, 15C, and 15D various low/high probability distributionsused in operation 1005 and elsewhere. FIG. 15A depicts new-measurementdistribution 1500, defined by lower bound 1501, upper bound 1503, lowerbound uncertainty 1502, and upper bound uncertainty 1504, and obtainedin accordance with operation 1001. FIG. 15B depicts logarithmicdistribution 1510, which is the logarithmic representation of lineardistribution 1500, transformed as described below and in regard tooperation 1401. FIG. 15C depicts logarithmic distribution 1520, which isthe logarithmic representation of a previous version of distribution1530 and that had been obtained in a previous iteration of operation1005. FIG. 15D depicts updated distribution 1530, a linear distribution,which is the result of adding distributions 1510 and 1520 and thenapproximating a linear distribution, as described below.

In accordance with operation 1401, location engine 113 transforms, intologarithmic representations, new-measurement distribution 1500, storedin accordance with operation 1111, and a version of probabilitydistribution 1530 from a previous iteration of operation 1401, which wasstored in accordance with a previous iteration of operation 1407described below. The logarithmic transformation results in distributions1510 and 1520, respectively.

The rationale for the transformation is now explained. As describedabove, location engine 113 multiplies two low/high distributions inorder to produce an updated distribution. In order to multiply twolow/high distributions, it can be simpler to work with the log of thedistributions, since the addition of two log distributions is theequivalent of the multiplication of two linear representations. Thelogarithmic representation of a low/high distribution has a flat top asbefore, but with linearly sloping sides instead of exponentiallydecaying sides.

In accordance with operation 1403, location engine 113 adds the two logdistributions together. The addition of two log distributions is apiecewise linear function that is also concave downward.

In accordance with operation 1405, location engine 113 generates anupdated probability distribution. This requires approximating the resultof operation 1403 back into a linear representation of a low/highdistribution. This approximating is necessary because the result ofoperation 1403 is not a true low/high distribution, even though itappears to be.

In order to approximate the result of operation 1403 back into alow/high distribution, location engine 113 uses a variant of the k-meansclustering algorithm described in Magnani, A. & Boyd, S. P. “Convexpiecewise-linear fitting,” Optimization and Engineering, March 2009,Volume 10, Issue 1, pp 1-17, incorporated by reference herein. Thevariant is summarized here. Location engine 113 samples the exact logdistribution (e.g., with 200 samples) over the interval where the logdistribution is no less the maximum (e.g., by two). Engine 113 thengives an initial assignment of which samples belong the three groupsconsisting of the flat top, the left (lower) slope, and the right(upper) slope. To refine the assignment, engine 113 takes the best fitlines for each of the three groups; for the flat top, engine 113 takesthe average y-value. Then, the resulting low/high approximation is thepointwise minimum (the lower envelope) of these three best fit lines,with the new assignment for the samples being determined by the newlow/high approximation. The process of approximating is iterated untilthe sample assignment does not change.

The result of operation 1405 is depicted in FIG. 15D, depictingdistribution 1530, defined by lower bound 1531, upper bound 1533, lowerbound uncertainty 1532, and upper bound uncertainty 1534.

In accordance with operation 1407, location engine 113 stores an updatedprobability distribution probability distribution 1530, defined by thelower bound, upper bound, lower bound uncertainty, and upper bounduncertainty.

Control of task execution then passes to operation 907.

Operation 907: Determine and Store an Updated Estimate of MeasurementBias—FIG. 16 depicts a flowchart of the salient processes performed inaccordance with operation 907.

In accordance with operation 1601, location engine 113 combines theupper and lower bounds of pressure bias obtained in accordance withoperation 905, result in an updated estimate of the pressure measurementbias of wireless terminal 101. In accordance with the illustrativeembodiment, location engine 113 bases the updated estimate on themidpoint (i.e., mean) of lower bound 1531 and upper bound 1533. In somealternative embodiments of the present invention, location engine 113bases the updated estimate on the mean of the overall shape of updateddistribution 1530, including lower tail 1532 defined by the loweruncertainty and upper tail 1534 defined by the upper uncertainty.

In accordance with operation 1603, location engine 113 stores theupdated estimate of bias as part of a series of estimates of bias ofbarometric pressure at wireless terminal 101, wherein the series furthercomprises estimates of bias generated in previous or subsequentiterations of operation 403. Location engine 113 can analyze (e.g.,perform trend analysis on, etc.) the series of estimates of bias inorder to determine whether additional calibration is needed inaccordance with operation 403.

In some embodiments of the present invention, location engine 113performs calibration of wireless terminal 101's barometer repeatedly(e.g., periodically, sporadically, on-demand, etc.), in order to accountfor any drift of the barometric pressure measurements. Drift can beattributed to the aging of the barometric sensor and other possiblecharacteristics (e.g., temperature, humidity, etc.), temporal-dependentor otherwise, and is often reflected in the trend of the estimates ofbias stored at operation 1603. In some embodiments of the presentinvention, location engine 113 triggers re-calibration based on apredefined change in temperature and/or humidity measured by wirelessterminal 101, over a period of time.

After operation 1603, control of task execution proceeds to operation405.

Operation 407: Collect Temperature and Barometric Measurements—FIG. 17depicts a flowchart of the salient processes performed in accordancewith operation 407 and operation 903.

In accordance with operation 1701, airport pressure station 114 measuressamples of temperature, T_(W), and barometric pressure, P_(W), in itsvicinity. In some embodiments of the present invention, each samplerepresents one measurement of temperature or of barometric pressure,while in some other embodiments each sample comprises more than onemeasurement of temperature or of barometric pressure.

In accordance with operation 1703, airport pressure station 114transmits a measurement of temperature, T_(W), (i.e., provides ameasurement of temperature at the outdoor location of station 114) andatmospheric pressure, P_(W), (i.e., provides a measurement of barometricpressure at the outdoor location of station 114) to location engine 113.In accordance with the illustrative embodiment, operation 1703 isperformed every 10 minutes, but it will be clear to those skilled in theart how to make and use alternative embodiments of the present inventionthat transmit the measurements at other times.

In accordance with operation 1705, location engine 113 receives themeasurement of temperature, T_(W), and a measurement of atmosphericpressure, P_(W), transmitted in accordance with operation 1703.

In accordance with operation 1707, wireless terminal 101 measuressamples of temperature, T_(T), and barometric pressure, P_(T), in itsvicinity by using barometer 205. In some embodiments of the presentinvention, each sample represents one measurement of temperature or ofbarometric pressure made by wireless terminal 101, while in some otherembodiments each sample comprises more than one measurement oftemperature or of barometric pressure made by the wireless terminal. Inaccordance with the illustrative embodiment, a measurement oftemperature or of barometric pressure is taken once per second, but itwill be clear to those skilled in the art how to make and usealternative embodiments of the present invention that take themeasurements at a different rate (e.g., 5 per second, 10 per second,etc.).

In accordance with operation 1709, wireless terminal 101 transmits ameasurement of temperature, T_(T), and a measurement of atmosphericpressure, P_(T), to location engine 113. In accordance with theillustrative embodiment, operation 1709 is performed every 5 seconds,but it will be clear to those skilled in the art how to make and usealternative embodiments of the present invention that transmit themeasurements at other times.

In accordance with operation 1711, location engine 113 receives thetemperature and atmospheric measurements transmitted in accordance withoperation 1709. In some embodiments of the present invention, locationengine 113 combines the values of multiple pressure samples (e.g., bycalculating a median, etc.) in order to reduce measurement noise.

Operations 1701 through 1711 are performed continuously, concurrently,and asynchronously, in accordance with the illustrative embodiment.

Operation 409: Generate an Estimate of Elevation—FIG. 18 depicts aflowchart of the salient processes performed in accordance withoperation 409.

In accordance with operation 1801, location engine 113 corrects thecurrent pressure measurement P_(T) by applying to it the latest estimateof bias that is determined in accordance with operation 1601, resultingin corrected pressure measurement P_(B). It will be clear to those whoare skilled in the art, after reading this specification, how to apply(e.g., add, subtract, etc.) a single estimate of bias based on how theestimation process has been implemented.

In some embodiments of the present invention, one or more biases fromthe series of biases stored and maintained in accordance with operation1603, are applied to the current pressure measurement, for example, byan exponential average, a differently weighted average, a straightaverage, and so on. In some embodiments of the present invention, theone or more biases are applied based on seasonal conditions or diurnalconditions.

In accordance with operation 1803, location engine 113 generates anestimate of the elevation of wireless terminal 101 that is based onpressure data and outdoor scale height. The estimate, Z_(T), is basedon:

$\begin{matrix}{Z_{T} = {{{- H_{OUT}} \cdot {\ln ( \frac{P_{B}}{P_{W}} )}} + Z_{W}}} & ( {{Eq}.\mspace{11mu} 4} )\end{matrix}$

wherein:

-   -   Hour is the outdoor scale height of the atmosphere, which is the        elevation at which the atmospheric pressure has decreased to e⁻¹        times its value at mean sea level (e.g., approximately 8400        meters) and is based on outdoor temperature, T_(W).    -   P_(B) is the relevant measurement of barometric pressure        received from wireless terminal 101 corrected for measurement        bias in accordance with operation 1801,    -   P_(W) is the measurement of atmospheric pressure at airport        pressure station 114 (in Pascals), and    -   Z_(W) is the elevation of airport pressure station 114.

In some embodiments of the present invention, measurements P_(T) andP_(W) are used that coincide in time with T_(T) and T_(W) as closely aspossible. In accordance with the illustrative embodiment, locationengine 113 has access to multiple airport pressure stations, such asairport pressure station 114, and uses a pressure measurement P_(W) fromthe particular airport pressure station that is the closest in distanceto the lateral location estimated in accordance with operation 405. Insome embodiments of the present invention, location engine 113 usesmeasurements from the airport pressure station that is most relevant tothe lateral location estimated in accordance with operation 405, in someway other than being closest in distance.

As those who are skilled in the art will appreciate after reading thisspecification, in some alternative embodiments Z_(T) can be determinedusing a different equation than that described above. Additionally, insome embodiments of the present invention Z_(T) can also be based on thelateral location of wireless terminal 101 estimated in accordance withoperation 405. In some embodiments of the present invention, locationengine 113 accounts for indoor and/or outdoor temperatures, stackeffects in a building, and so on.

It is to be understood that the disclosure teaches just one example ofthe illustrative embodiment and that many variations of the inventioncan easily be devised by those skilled in the art after reading thisdisclosure and that the scope of the present invention is to bedetermined by the following claims.

What is claimed is:
 1. A method of estimating the elevation of awireless terminal, the method comprising: receiving, by a dataprocessing system, a first estimate of location of a wireless terminal;receiving, by the data processing system, a first measurement ofbarometric pressure at the wireless terminal; generating, by the dataprocessing system, data points in a nonempty first set of data points inspace based on the first estimate of location of the wireless terminal,wherein the data points correspond to geographical coordinates;generating, by the data processing system, a first probabilitydistribution of pressure measurement bias defined by: (i) a firstestimate of bias of barometric pressure measured by the wirelessterminal, wherein the first estimate of bias is based on (a) a firstdata point whose geographical coordinates are at the lowest elevation inthe first set of data points, and (b) the first measurement ofbarometric pressure at the wireless terminal, and (ii) a second estimateof bias of barometric pressure measured by the wireless terminal,wherein the second estimate of bias is based on (a) a second data pointwhose geographical coordinates are at the highest elevation in the firstset of data points, and (b) the first measurement of barometric pressureat the wireless terminal; receiving, by the data processing system, asecond measurement of barometric pressure at the wireless terminal; andgenerating, by the data processing system, an estimate of the elevationof the wireless terminal based on (a) the second measurement ofbarometric pressure at the wireless terminal, and (b) the firstprobability distribution of pressure measurement bias.
 2. The method ofclaim 1 further comprising transmitting the estimate of elevation of thewireless terminal to a location-based application server.
 3. The methodof claim 1 wherein the first probability distribution of pressuremeasurement bias is further defined by (i) a first uncertainty thatcharacterizes an exponential decay from the first estimate of biastoward a first end of the first probability distribution, and (ii) asecond uncertainty that characterizes an exponential decay from thesecond estimate of bias toward a second end of the first probabilitydistribution.
 4. The method of claim 1 wherein the data points aredefined by a normal distribution along a horizontal dimension, andwherein the first estimate of location comprises a first geographicalcoordinate whose value defines the mean of the normal distribution. 5.The method of claim 1 wherein the estimate of the elevation of thewireless terminal is further based on an average of (i) the firstestimate of bias and (ii) the second estimate of bias.
 6. The method ofclaim 1 further comprising: receiving, by the data processing system, aseries of prior measurements of barometric pressure at the wirelessterminal made prior to the first measurement of barometric pressure atthe wireless terminal; generating, by the data processing system, asecond probability distribution of pressure measurement bias defined by:(i) a lower estimate of bias of barometric pressure measured by thewireless terminal, wherein the lower estimate of bias is based on theseries of prior measurements of barometric pressure, and (ii) an upperestimate of bias of barometric pressure measured by the wirelessterminal, wherein the upper estimate of bias is based on the series ofprior measurements of barometric pressure; and generating, by the dataprocessing system, an updated probability distribution of pressuremeasurement bias, based on combining mathematically the firstprobability distribution and the second probability distribution;wherein the estimate of the elevation of the wireless terminal isfurther based on the updated probability distribution of pressuremeasurement bias.
 7. A method of estimating the elevation of a wirelessterminal, the method comprising: receiving, by a data processing system,a series of measurements of barometric pressure at the wirelessterminal; generating, by the data processing system, a first probabilitydistribution of pressure measurement bias, based on the series ofmeasurements of barometric pressure at the wireless terminal; receiving,by a data processing system, a first estimate of location of a wirelessterminal; receiving, by the data processing system, a first measurementof barometric pressure at the wireless terminal; generating, by the dataprocessing system, data points in a nonempty first set of data points inspace based on the first estimate of location of the wireless terminal,wherein the data points correspond to geographical coordinates;generating, by the data processing system, a second probabilitydistribution of pressure measurement bias defined by: (i) a firstestimate of bias of barometric pressure measured by the wirelessterminal, wherein the first estimate of bias is based on (a) a firstdata point whose geographical coordinates are at the lowest elevation inthe first set of data points, and (b) the first measurement ofbarometric pressure at the wireless terminal, and (ii) a second estimateof bias of barometric pressure measured by the wireless terminal,wherein the second estimate of bias is based on (a) a second data pointwhose geographical coordinates are at the highest elevation in the firstset of data points, and (b) the first measurement of barometric pressureat the wireless terminal; receiving, by the data processing system, asecond measurement of barometric pressure at the wireless terminal; andgenerating, by the data processing system, an estimate of the elevationof the wireless terminal based on (a) the second measurement ofbarometric pressure at the wireless terminal, (b) the first probabilitydistribution of pressure measurement bias, and (c) the secondprobability distribution of pressure measurement bias.
 8. The method ofclaim 7 further comprising transmitting the estimate of elevation of thewireless terminal to a location-based application server.
 9. The methodof claim 7 wherein the first estimate of location of the wirelessterminal comprises geographical coordinates in two horizontaldimensions.
 10. The method of claim 7 wherein the second probabilitydistribution of pressure measurement bias is further defined by (i) afirst uncertainty that characterizes an exponential decay from the firstestimate of bias toward a first end of the second probabilitydistribution, and (ii) a second uncertainty that characterizes anexponential decay from the second estimate of bias toward a second endof the second probability distribution.
 11. The method of claim 7wherein the data points are defined by a normal distribution along ahorizontal dimension, and wherein the first estimate of locationcomprises a first geographical coordinate whose value defines the meanof the normal distribution.
 12. The method of claim 11, furthercomprising receiving an uncertainty in the first estimate of location ofthe wireless terminal, wherein a horizontal component of the uncertaintyin the first estimate of location defines the standard deviation of thenormal distribution.
 13. The method of claim 7 further comprisingcombining mathematically the first and second probability distributionsof pressure measurement bias, resulting in an updated probabilitydistribution of pressure measurement bias defined by (i) a lowerestimate of bias of barometric pressure measured by the wirelessterminal and (ii) an upper estimate of bias of barometric pressuremeasured by the wireless terminal, wherein the updated probabilitydistribution is flat between the lower and upper estimates of bias. 14.The method of claim 13 wherein the estimate of the elevation of thewireless terminal is further based on an average of (i) the lowerestimate of bias of barometric pressure measured by the wirelessterminal and (ii) the upper estimate of bias of barometric pressuremeasured by the wireless terminal.
 15. A method of estimating theelevation of a wireless terminal, the method comprising: receiving, by adata processing system, a first estimate of location of a wirelessterminal, the first estimate comprising i) a first geographic coordinatevalue along a first horizontal dimension and ii) a second geographiccoordinate value along a second horizontal dimension; receiving, by thedata processing system, a first measurement of barometric pressure atthe wireless terminal; generating, by the data processing system, datapoints in a nonempty first set of data points in space, based on i) afirst normal distribution that is defined by the first geographiccoordinate value and ii) a second normal distribution that is defined bythe second geographic coordinate value, wherein the data points in thefirst set are represented by coordinate values along the first andsecond horizontal dimensions; generating, by the data processing system:(i) a first estimate of bias of barometric pressure measured by thewireless terminal, based on (a) a first data point whose geographicalcoordinates are at the lowest elevation in the first set of data points,and (b) the first measurement of barometric pressure at the wirelessterminal, and (ii) a second estimate of bias of barometric pressuremeasured by the wireless terminal, based on (a) a second data pointwhose geographical coordinates are at the highest elevation in the firstset of data points, and (b) the first measurement of barometric pressureat the wireless terminal; receiving, by the data processing system, asecond measurement of barometric pressure at the wireless terminal; andgenerating, by the data processing system, an estimate of the elevationof the wireless terminal based on (a) the second measurement ofbarometric pressure at the wireless terminal, (b) the first estimate ofbias, and (c) the second estimate of bias.
 16. The method of claim 15further comprising transmitting the estimate of elevation of thewireless terminal to a location-based application server.
 17. The methodof claim 15 wherein the first estimate of location further comprises anuncertainty in the first geographic coordinate value, wherein at leastone of the first normal distribution and the second normal distributionis further defined by the uncertainty in the first geographic coordinatevalue.
 18. The method of claim 17 wherein the first coordinate valuedefines the mean of the first normal distribution, and wherein theuncertainty in the first geographic coordinate value defines thestandard deviation of the first normal distribution.
 19. The method ofclaim 15 wherein the estimate of the elevation of the wireless terminalis further based on an average of (i) the first estimate of bias and(ii) the second estimate of bias.
 20. The method of claim 15, furthercomprising: defining a first probability distribution of pressuremeasurement bias by (i) the first estimate of bias of barometricpressure measured by the wireless terminal and (ii) the second estimateof bias of barometric pressure measured by the wireless terminal,wherein the first probability distribution is flat between the first andsecond estimates of bias; receiving, by the data processing system, aseries of prior measurements of barometric pressure at the wirelessterminal made prior to the first measurement of barometric pressure atthe wireless terminal; and combining mathematically the firstprobability distribution of pressure measurement bias and a secondprobability distribution of pressure measurement bias, wherein thesecond probability distribution is based the series of priormeasurements of barometric pressure.